RF formulas1
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Transcript of RF formulas1
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urce free region
th current and
arge densities 0
characteristic imp
These are all peak formulas....rm
formulas will hav 1/2 owing to rcurrent and voltage each
gamma changes only in
ase as we go away frm
ad...remember constSWR circle...
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Note that gamma L might becomplex in itself...but then
again at dist x mag is stillm|
gammaL|
horn dimentions
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Electric Field at
dist R fromantenna
Deciding where far field lies
use to calculate max electric
field at a certein distance
n0=377 ohm
Parabolic antenna: Effective areafor 55% efficiency
HORN gain
This followsfrom BW in
each of the
planes
Parabolic Antenna Gain and
HPBW(expect a fewthousands of magnitude)
Isotropic
radiator: Pt
is powerfed toantenna
(Pdelivered
) via tx lineor w/g
For antenna same as
any other load
Any mention of power reflection and
transmission percentage points to gamma
DIPOLE1.64 is the derived standard gainfor a dipole
Rough
estimate of
3dB
Beamwidthfor High gain
Ant(use K1~70o
)...D isaperture
dimention in
plane in
consideration
Condition for cutoff freq of
antenna and hence BW(11%reflection) Use RL chart
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Step#5Get
Rin from this
Step#4Length of pat
Step#6Matching to 50 ohm linewith Qwave txfrmr(which is againuStrip..so use wheeler for w/h)
keep h same as tht of patch length
of Qwave is offcourse lambdag /4
Illustration 1:
Circular Horn
ircular Horn Design
power density for
nonisot radiator
gain in terms ofeffective aperture
Directivity
Gain is prod of DIRmax and
aperture efficiency, hence amore coplete discription of its
performance
i=indi mag.//phi= feed phase
rogression(0,phi, 2*phi...)
In fig below, theta0 is the p
front(corres to line joining
equiphase pts)...and logicavarying phi, we get diff the
Step#2^^
PATCH ANTENNA DESIGN>>
No gain constraints but matching is priority
Plug in step#5This isnot gain...its
susceptance
Step#1
Step#3The only parameters given e.g. are these
3dB BW With
Halfwavelength
Spacing(good 2 avoidgrating ie sidelobes)
ray factor...2d array has 2
oduct of such summ terms
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___________________________________________________________________________________
Take loss as -ve in dB gain domain
MDS at o/p....at i/p its just kTB in dBm
+3dB
intermodulation freqs at
o/p of a mixer
imp: o/p noise of 1st stage incascade sys this is then I/p to
stage 2
Illustration 2: spuriusfreq,,,
Illustration 3: Power amp
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NOISE
regenerative mixer type freq divider
Microwave Couplers
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Wave leaves radar:
ove is relation betn
erture and gain
#2: pwr
density
neartarget
#3RCS
#5max distance bysubstituting min allowed
pwr
#7: replace Aer with formula
in Gr#8:Si(min) is nothing but M
Pulse radar formulae
#4capture by radar
#6: a combined
version finallywith Gt=Gr=G
Illustration B=BW
of radar
#4 backscatter
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Chapter6
Numerator is difference betn the carr pwr nd
noise pwr at freq fm near carr...
FM and phase both noises produce noise
sidebands arnd carr
amount of FM(or Phase) noise present is written
wrt. Carr always ie dBc(ie similar 2 calculating
dBm except that one has to norm wrt carr pwrhere by takin 10log)
Illustration 4: To improve the stability, one can use (1) high-Qcircuits to build the oscillators (examples are waveguide
cavities, dielectric resonators,or superconducting
resonators=cavities); (2) temperature compensation circuits;or(3) phase-locked oscillators or frequency
synthesizersFEEDDWD AMP: Used to avoid IM products in
amp: basically produces -ve IM1 and IM2 frm signal itself and
then adds them 2 signal 2 cancel IM1 and IM2
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For a VCO with vtg range in
deno.
Crystal Equivalent ckt formulae
colpitt's crystal osc:a)series b) || resonant config....used
as reference for PLOs
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R=c*tR/2...tR is shown andfound as= (freq variatn/slope)
ie x=y/m slope is
2*deltaF*fm.....hence tR isfR/slope
fR is middle of (average) two fb s we get
while doppler shift is found like this
find velocity
from fd...notethat this is
cosine of
actual velocity
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An error signal will be generated if the antenna beam is
not exactly on the target. This error signal will be used to control a servomotor to align the antenna to
the target. There are three methods for generating the errorsignal for tracking:
1. Sequential lobing
2. Conical scan3. Monopulse
Sequential lobing....whichever voltage is greater move antt towards tht
side
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beam rotated at Wm....if its not aligned, return s/g is AM
power divided betn 2 or 4 antenna....alignment results only if
all antt recieve same vtg...2 antt give only 1D tracking 4 anttgive 2D tracking
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Illustration 5: Friss for Link Budget..Lsys
includes antenna feed mismatch, pointingerror, atmospheric loss, and polarization loss
it can be seen that the range is doubled if the output power is
increased four times. In the radar system, it would require the output power be
increased by 16 times to double the operating distance
Also it can be seen that the receiver output SNR ratio can be
increased if the transmission distance is reduced. The increase in transmitting power
or antenna gain will also enhance the output SNR ratio as expected
Steps to Friis
deriving spaceloss(atmospheric loss is diff
from space loss)
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Hence it can be said that BER performance of any system is probability that noise will take value sohigh as to make RV N+Si go into region of other symbol Sj
BPSK constellation
Deriving BPSK BER
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We plot Pe vs Eb/No...Eb/No is one valued description of channel and conditions in generalHigh Eb/No ie S/g energy results in better performance and vice versa...thats why graph is decreasing
for all modula schemes
Pe will depend on Euclidean Distance between symbol points in constellation
Modulation and more
Illustration 9: BPSK
Illustration 8: BFSK
Illustration 7: ASK
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tration 6: if n is no of symbols and M is
ber of bits, then M is B/W efficiency(M note confu with privious use of M)
tical purposes due to BER performance^^
why we dont go for infinite -aryulation
So, knowing capacity and bandwidth, one can find wat maximum M-ary system can be used...as weknow, as M increases constellation becomes crowded and probability of error increases